caa a22 4500 463177630 CHVBK 20180406164829.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s10596-006-9035-5 doi (NATIONALLICENCE)springer-10.1007/s10596-006-9035-5 Application of the representer method for parameter estimation in numerical reservoir models [Elektronische Daten] [Justyna Przybysz-Jarnut, Remus Hanea, Jan-Dirk Jansen, Arnold Heemink] A data assimilation method was applied to estimate poorly known parameters (permeabilities) in a numerical reservoir model. Most variational methods for data assimilation are based on the assumption that the model is perfect except for the poorly known parameters. The representer method allows also for model errors, i.e. for uncertainties in the state variables (pressures and saturations). The method is based on minimizing a cost functional, assuming all the errors and parameters to be multivariate Gaussian random variables with given mean and covariances. The uncertain parameters and variables are expanded into a finite sum of basis functions called representers, and the gradients of the cost functional are obtained with an adjoint method. This approach gives an optimal parametrization in the sense that the final result is equal to the solution of the full inverse problem. The method was tested on a simple one-dimensional model to simulate two-phase (oil-water) flow through a heterogeneous reservoir. The results show that the method is able to provide an acceptable estimate of the permeability field. We used pressure measurements from a small number of observation wells in between the injection and production wells, but the representer method could be used equally well to assimilate data from other sources. The method appears to be a promising data assimilation tool for applications in reservoir engineering. Springer Science+Business Media, Inc., 2006 adjoint method nationallicence automatic history matching nationallicence Euler-Lagrange equations nationallicence one-dimensional two-phase flow nationallicence representer method nationallicence Przybysz-Jarnut Justyna Laboratory of Acoustical Imaging and Sound Control, 2600 GA Delft, Lorentzweg 1, P.O. Box 5046, 2628 CJ, Delft, The Netherlands aut Hanea Remus Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands aut Jansen Jan-Dirk Faculty of Civil Engineering and Geosciences, Department of Geotechnology, Delft University of Technology, Delft, The Netherlands aut Heemink Arnold Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands aut Computational Geosciences Kluwer Academic Publishers 11/1(2007-03-01), 73-85 1420-0597 11:1<73 2007 11 10596 https://doi.org/10.1007/s10596-006-9035-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10596-006-9035-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Przybysz-Jarnut Justyna Laboratory of Acoustical Imaging and Sound Control, 2600 GA Delft, Lorentzweg 1, P.O. Box 5046, 2628 CJ, Delft, The Netherlands aut NATIONALLICENCE 700 1- Hanea Remus Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands aut NATIONALLICENCE 700 1- Jansen Jan-Dirk Faculty of Civil Engineering and Geosciences, Department of Geotechnology, Delft University of Technology, Delft, The Netherlands aut NATIONALLICENCE 700 1- Heemink Arnold Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands aut NATIONALLICENCE 773 0- Computational Geosciences Kluwer Academic Publishers 11/1(2007-03-01), 73-85 1420-0597 11:1<73 2007 11 10596 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer